Augmented matrix

Determine whether there is a unique solution, no solution, or an infinite set of solutions with one or two parameters.

I'm supposed to use an augmented matrix to solve this. (I don't know how to make the augmented part of the matrix.)
When reducing the matrix, I get a row of zeros, so this means that there is a line of intersection for the planes, so an infinite set of solutions dependent on one parameter.
But the answer says that there is no solution.

The key is in the augmented matrix. When you do elementary row operations, you also have to do them on the solution vector. When you do that, notice what number corresponds to the row with all zeros in it.

The latter is true. There is no way that 0x + 0y + 0z = -2. There are no values of x, y, and z that can make that true. Hence, there is no solution. This is typically what a linear system looks like that has no solution. Make sense?